I would love some tips on how to structure my resume/cv. I have taught for 8 years and 3 of which were international. My last year teaching international ended up with me getting sacked at the end of the year (it seemed more personal than professional). I returned to the states and spent the last two years working at the same school.

How do I handle this experience when creating my resume and during interviews?

Well, that could seriously cramp your recruitment options. If you were out and out fired, many schools will shy away from you (unless the admin/school that fired you has a widely known and really poor reputation).

You only real choices seem to be spin it, or ghost it. If you leave it on your CV, potential schools will likely contact the school/admin for a reference and what they say may blow up many otherwise likely opportunities. So, in that case, think of how you could spin the experience so as to minimize the damage. This would take place in an interview rather than on your CV. You could try to spin it as a mutual parting of the ways, personality conflict with admin, etc. None of which is really great (especially if the admin in question will strongly contradict that view) but not necessarily a deal breaker if they otherwise like you as a person/candidate. Is there anyone else at the school that you could list as a reference that would give you a better/different report?

Your other choice is to just leave it as a gap with a reasonable explanation (studying, traveling, taking care of family, etc.). This is easier to pull off if it is only one year (and obviously gets harder/less feasible for every year thereafter). This option has its risks but you would not be the first to try it and land on their feet.

On the upside, you have two years of post-sacking (presumably/hopefully successful) experience you can play up/highlight. Other posters may have more useful advice for you. Good luck with however you choose to handle it!

I thought about ghosting it, but I have ethical issues about it. I added it to my Search profile along with two references, two years ago and have thought to delete it from my profile, but wasn't sure if Search monitors such things.

My department head provided a strong reference for me though and I use him as my reference from that experience (the admin has since left the school). The admin who made the call on me gave me a letter of reference and told me to spin it as "not a great fit," and leave it at that. In interviews, I spin it as my then partner/now wife had problems getting a visa in the country which is true.